COMP. JUST CUTS OFF AND EVERYTHING GOES DEAD. BLUE

Power Supply is the highly probable culprit on this. Call your local manufacturer to replace the power supply. Also, try connecting it directly to the power outlet (if it's connected to a power strip). Also, check the fans on the computer. All should be spinning and air should be coming out of it. Feel the air coming out, is it warm or hot. If it's hot then I suggest you really call your computer manufacturer or who you got this from since this needs more troubleshooting and probable replacement of parts inside.

Check the fan if any on the processor. See if it is working.
This sounds like a heat problem.

One quick way to determine heat shut down.
Take the side cover off, (The one where you can access the processor and memory). Take a fan and aim it toward the computer.
If the machine keeps running you only need to clean and maybe add another fan to the box. If it is the fan on top of the processor that has stopped working. It will most likely die again. Just be sure the fan on the processor is clean and working.
If not replace fan and clean heat sink. It is really not difficult.
Just do not remove the processor! You may bend those delicate pins.

The power supply also has a fan that circulates air.
Use one of those canned air things and blow the vents out.
DO NOT let the fan spin wildly while doing this. (can damage the bearings). Just hold a pencil or anything to stop the fan from spinning while you clean. Make certain you do all this with the machine unplugged!

Canned air works well on the Process fan and heat sing too!

Good luck!
Hope this helps!